The use of stem cell therapy for multiple sclerosis has been previously reported in case reports, including from Dr. Simon Slavin's group in Israel.
In multiple sclerosis the rationale for why stem cell therapy would have beneficial effects derives from observations that some types of stem cells, such as mesenchymal stem cells, are potent stimulators of immune regulatory T cells called "T Regulatory Cells", or back in the old days they were called "T Suppressor Cells". These cells selectively inhibit certain immune responses, while allowing other immune responses to exist. Why this is important is because many scientists believe that multiple sclerosis is an "autoimmune disease", that meaning that the immune system is attacking parts of the body. In the example of multiple sclerosis, the target antigen appears to be myelin basic protein, a protein that lines the nerves and allows for them to properly conduct signals.
In addition to play a role in suppressing inflammatory responses, mesenchymal stem cells are known to produce various factors that are theoretically useful for remyelination, that is, repairing the injured sheath of the nerve.
The video describes two patients that have been treated with stem cell therapy and report positive benefits. Obviously we will not know the scientific validity of these claims until clinical trials are conducted, however, given the relative safety profile demonstrated by Osiris therapeutics for mesenchymal stem cells, these experimental interventions may serve as an ethical source of critically important data on the biology and immunology of stem cell therapy.